Problem: The grades on a history midterm at Springer are normally distributed with $\mu = 83$ and $\sigma = 3.5$. Ashley earned a n $88$ on the exam. Find the z-score for Ashley's exam grade. Round to two decimal places.
Explanation: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Ashley's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{88 - {83}}{{3.5}}} $ ${ z \approx 1.43}$ The z-score is $1.43$. In other words, Ashley's score was $1.43$ standard deviations above the mean.